任意三角形内角和定理的几何证明演示

GeoGebra 命令及参数

1. Polygon(A, B, C) → P, c, a, b
2. Midpoint(B, A) → D
3. Midpoint(A, C) → E
4. Midpoint(B, C) → F
5. Polygon(B, F, D) → Q, d, b_1, f
6. Polygon(A, D, E) → R, e, a_1, d_1
7. Polygon(F, C, E) → S, e_1, f_1, c_1
8. Midpoint(B, F) → G
9. Rotate(B, α, G) → B'
10. Rotate(F, α, G) → F'
11. Rotate(D, α, G) → D'
12. Polygon(B', F', D') → Q', d', b', f'
13. Midpoint(F, C) → H
14. Rotate(F, (-α), H) → F'_1
15. Rotate(C, (-α), H) → C'
16. Rotate(E, (-α), H) → E'
17. Polygon(F'_1, C', E') → S', e', f'_1, c'
18. Vector((A * α / 3.14), (F * α / 3.14)) → u
19. Translate(A, u) → A'
20. Translate(D, u) → D'_1
21. Translate(E, u) → E'_1
22. Polygon(A', D'_1, E'_1) → R', e'_1, a', d'_1
23. Angle(F', B', D') → β
24. Angle(E', C', F'_1) → γ
25. Angle(D'_1, A', E'_1) → δ